CN109544578B - Three-dimensional fragment recombination restoration method based on maximum similarity matching - Google Patents

Three-dimensional fragment recombination restoration method based on maximum similarity matching Download PDF

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CN109544578B
CN109544578B CN201811450882.6A CN201811450882A CN109544578B CN 109544578 B CN109544578 B CN 109544578B CN 201811450882 A CN201811450882 A CN 201811450882A CN 109544578 B CN109544578 B CN 109544578B
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孙进
丁煜
王宁
张道周
张洋
朱兴龙
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Yangzhou University
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Abstract

A three-dimensional fragment recombination restoration method based on maximum similarity matching belongs to the technical field of computer engineering and cultural relic restoration engineering. The method includes the steps that a three-dimensional laser scanner is used for collecting point cloud data of three-dimensional fragments, firstly, a curved surface is constructed based on the point cloud and an adjacent region of the point cloud, the bending degree of the curved surface is calculated, so that a contour curve of a three-dimensional fragment fracture surface is extracted, then, the adjacent region area on the contour curve of the fracture surface is calculated to describe the concave-convex property of the contour curve of the fracture surface, then, the similarity of the contour curve of the fracture surface is calculated by searching fuzzy common segments, and finally, the three-dimensional fragments are aligned and spliced by adopting an iterative closest point algorithm, so that a three-dimensional recovery model is obtained. The method does not need to rely on any hypothesis about the geometric shape of the original object or excessively rely on the determination of the threshold, has strong independence and applicability, and is more stable and accurate in algorithm.

Description

Three-dimensional fragment recombination restoration method based on maximum similarity matching
Technical Field
The invention relates to a splicing method of three-dimensional broken objects, in particular to a three-dimensional fragment recombination restoration method based on maximum similarity matching, and belongs to the technical field of computer engineering and cultural relic restoration engineering.
Background
Chinese nationality has thousands of years of civilization history, and many cultural heritages hidden under rivers, lakes and oceans. According to the data display of the national cultural relic administration underwater cultural heritage protection center, 241 underwater cultural relics are confirmed in China, and the protection and repair work of the underwater cultural relics is very important. The underwater cultural relics are mostly broken and incomplete after long-time erosion and jolt at the bottom, and a large amount of broken cultural relics found by archaeological personnel in underwater sites are mainly restored by hands at present, so that the defects of long splicing period, large error, easy secondary damage to the cultural relics in the operation process and the like are overcome. In the face of the situation that archaeological professional repair personnel are extremely short and the situation that the historical relic is required to be spliced and restored by a blowout, the virtual splicing of the broken historical relics is realized by utilizing the computer-assisted historical relic restoration technology, and practice proves that the difficulty of restoration of the historical relics can be reduced, the splicing speed is accelerated, and the secondary damage to the historical relics in the repair process can be avoided.
The three-dimensional object randomly forms a plurality of sub-objects with arbitrary shapes after being crushed, and if the sub-objects formed after being crushed have certain thicknesses, the sub-objects are called three-dimensional fragments. The three-dimensional fragment splicing algorithm can be substantially converted into the problem of irregular curved surface matching, and foreign scientific research institutions of colleges and universities such as Stanford university, brarelix technology university in Germany, japan and rock and university and domestic scientific research institutions of colleges and universities such as Qinghua university and northwest university have utilized computer-assisted cultural relic restoration technology to achieve good effects in the fields of multi-view splicing, reverse engineering, curved surface detection, three-dimensional model retrieval, medical application and the like. The studies of three-dimensional fragment stitching by these colleges can be broadly divided into two categories: the first type is based on face feature matching. The Forma Urbis Romae project group of Stanford university, USA (D.Koller et al, 2006) matches based on a variety of information including the engraving pattern of the fragment surface, the wall features of the fragment, and the geometric features of the fragment edge, but only a few Fragments can be spliced up to now because of the lack of Fragments themselves. Huang QX et al, the university of Qinghua, in the text of Reassembling Fratured Objects by geometrical Matching (2006), first describe a plurality of geometrical characteristics of a segmented surface by using feature strings by using integral invariant, match fracture surfaces according to the plurality of feature strings by using a forward search algorithm, and finally perform overall splicing of fragments by using a subgraph fusion method, thereby better realizing automatic splicing recovery of complex fragments. In 2013, the Li shou of the northwest university takes the contour curve of the fracture surface as the characteristic for matching in the article "fracture rigid body restoration research based on fracture surface matching" of the Master graduate thesis, the method only searches for the characteristic information of the boundary points, is high in splicing speed, is suitable for matching fragments with a common boundary, but cannot perform correct matching on the fracture surface with smaller boundary superposition. The second category is based on point feature matching. Simon Winkelbach et al, university of Brennk technology, germany, in Pairwise Matching of 3D Fragments Using Cluster Trees (International Journal of Computer Vision,2008, 78 (1): 1-13), directly matches Fragments by Using a random sampling algorithm and a hierarchical binary tree according to all vertex information of fracture surfaces without extracting feature points, but the method is only suitable for complete Matching of fracture surfaces. Enkhbayar Altantsetseg et al of Japan, in Pairwise matching of 3D fragments using fast fourier transform (Visual Computer,2014, 30 (6-8): 929-38), introduces a new descriptor to represent clusters and curves of feature points, and then uses fast Fourier transform to complete Pairwise matching of three-dimensional fragments, wherein the feature points of the descriptor are obtained by curvature calculation, the descriptor of the curve is represented by Fourier series, and possible matching is found by comparing description curves of matching surfaces, but the splicing matching speed of the method is slow.
In view of the current research situation, the research on splicing recovery of three-dimensional broken objects is mainly focused on three-dimensional fragments, and the research on splicing matching of the three-dimensional fragments with thicknesses is less. The existing research method mainly splices the three-dimensional fragments according to the information of the fracture surfaces of the three-dimensional fragments, and the method has a good effect when restoring the cultural relics with complete fracture parts, but the restoration effect is too dependent on the size of the threshold value, the optimal value of the threshold value can be determined through multiple experiments and statistics, and if the size of the threshold value is not selected properly, a large splicing error is easy to occur.
Disclosure of Invention
In order to overcome the defects of the prior art and the method, the invention provides a three-dimensional fragment recombination restoration method based on maximum similarity matching, and the method can effectively improve the restoration effect of the three-dimensional fragment.
The invention aims to realize the method for reconstructing and restoring the three-dimensional fragments based on the maximum similarity matching, wherein a data processing object is point cloud data of the three-dimensional fragments acquired by a three-dimensional laser scanner, and the method comprises the following steps of:
step 1: calculating the bending degree of the curved surface based on the point cloud and the neighborhood structure curved surface thereof so as to extract a contour curve of the three-dimensional fragment fracture surface;
step 2: calculating the neighborhood area on the fracture surface contour curve, and describing the concave-convex property of the fracture surface contour curve based on the neighborhood area;
and step 3: searching fuzzy common segments of the fracture surface contour curve, and calculating the similarity of the fracture surface contour curve;
and 4, step 4: and (3) performing alignment splicing on the three-dimensional fragments by adopting an iterative closest point algorithm.
Preferably, the neighborhood area on the fracture surface contour curve is calculated in the step 2, the concave-convex property of the fracture surface contour curve is described based on the neighborhood area, and the following method is adopted, S r (p) the neighborhood area of a point p on the fracture surface profile curve is expressed, the neighborhood A of the point p is a circular area taking p as the circle center r as the radius and is marked as A r (p) of the formula (I). The integral function f (x) is a linear function, and f (x) =1 when the point x is outside the contour curve and f (x) =0 when the point x is inside the contour curve. Thus, the neighborhood area S of a point p on the fracture surface profile r (p) can be expressed as:
Figure BDA0001886638080000031
S r the geometric meaning of (p) is the circular area A r (p) the area of the outer part of the fracture surface profile, also called the neighborhood area. S r The value of (p) is proportional to the degree of irregularity of the profile curve in the vicinity of the point p and the magnitude of r, and A r (p) S of pairs of internal noise points r (p) size has no effect, S is seen r (p) reflects the degree of concavity and convexity of the fracture surface profile curve in the neighborhood of point p. When the point p is a convex vertex point,
Figure BDA0001886638080000032
when point p is a pit point, based on the number of pits, a decision is made as to whether the pit is present or not>
Figure BDA0001886638080000033
When point p is the vertex of a plane, then>
Figure BDA0001886638080000034
Preferably, in the step 3, fuzzy common segments of the fracture surface contour curve are searched, and the similarity of the fracture surface contour curve is calculated by the following method:
due to the complexity of the fracture surface contour curve and the error of discrete sampling, the probability of complete matching of the two contour curves is very small, the similarity of the fracture surface contour curve can be described by adopting a fuzzy common segment, and the fuzzy common segment refers to searching a section of curve with similar intervals in the two contour curves, provided that the interval distance cannot be too large. A contour curve E of fracture surface 1i There are m vertices, which can be denoted as
Figure BDA0001886638080000035
The neighborhood area of each vertex is calculated to obtain the characteristic sequence of the vertex as->
Figure BDA0001886638080000036
Another fracture surface contour curve E 2j There are n vertices that can be recorded as->
Figure BDA0001886638080000037
The characteristic sequence is obtained by the same way>
Figure BDA0001886638080000038
Profile curve of fracture surface E 1i The upper vertex->
Figure BDA0001886638080000039
And fracture surface profile curve E 2j Last vertex->
Figure BDA00018866380800000310
The similar distance of (c) can be expressed as:
Figure BDA00018866380800000311
finding a sequence of features
Figure BDA00018866380800000312
And a sequence of features
Figure BDA00018866380800000313
Length of fuzzy common fragment of (1)][j]And defining a fuzzy coefficient delta as the maximum separation distance allowed by the subscripts i and j, namely the number of times of different characteristic value situations allowed to occur between the two characteristic sequences, and controlling the matching precision of the two characteristic sequences by the fuzzy coefficient delta. Defining a fracture surface contour curve E 1i And fracture surface profile curve E 2j The similarity of (A) is as follows:
Figure BDA00018866380800000314
calculating a profile piecewise curve E 1i And a contour piecewise curve E 2j Because one fragment may have a plurality of fracture surfaces, the algorithm calculates the similarity between any two fracture surfaces of a pair of fragments, and selects the fracture surface with the highest similarity for the next alignment and splicing.
Compared with the prior art, the invention has the beneficial effects that: the reconstruction and restoration method of the three-dimensional fragment based on the maximum similarity matching has the advantages that the maximum similarity matching method for obtaining the fracture surface contour curve is defined and calculated, the method does not need to depend on any hypothesis about the geometric shape of an original object and excessively depend on the determination of a threshold value, the independence and the applicability are very strong, and the algorithm is more stable and accurate.
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FIG. 1 is a flow chart of the three-dimensional fragment reorganization restoration method based on maximum similarity matching according to the present invention;
FIG. 2 is a schematic diagram of the area of the neighborhood on the fracture surface contour line according to the present invention.
Detailed Description
The following describes the embodiment of the present invention with reference to fig. 1 and the method for reconstructing three-dimensional fragment based on maximum similarity matching.
As shown in FIG. 1, the three-dimensional fragment reorganization and restoration method based on maximum similarity matching of the invention comprises the following steps:
step 1: extracting contour curve of fracture surface based on curved surface bending degree
The method comprises the steps of collecting point cloud data of three-dimensional fragments by using a three-dimensional laser scanner, firstly constructing a curved surface based on the point cloud data and a neighborhood of the point cloud data, calculating the bending degree of the curved surface, then selecting points with the bending degree change of the curved surface larger than a certain threshold value in the point cloud as potential feature points, carrying out region segmentation on the potential feature points through a growing algorithm, then determining boundary points of feature point clouds in each segmented region through local curved surface reconstruction, carrying out iterative refinement on the boundary points by using a bilateral filtering algorithm based on the bending degree and distance of the curved surface, finally taking the refined boundary points as real feature points, and completing extraction of a fracture surface contour curve by establishing a minimum spanning tree of the feature points. For a three-dimensional point cloud W, the total content of the point cloud W is
Figure BDA0001886638080000041
Number of vertexes->
Figure BDA0001886638080000042
Wherein a certain vertex w φ Has the coordinate of (alpha) φ ,β φ ,γ φ ) Then the centroid W of the three-dimensional point cloud W c Comprises the following steps:
Figure BDA0001886638080000043
subtracting the point cloud center of mass W from the coordinate values of all vertexes contained in the three-dimensional point cloud W c Coordinate values of (a) to constructA 3 x 3 covariance matrix for the three-dimensional point cloud W is obtained:
Figure BDA0001886638080000044
by calculating the eigenvalue and eigenvector of the covariance matrix, 3 main directions of the point cloud data and the dispersion degree, lambda, in the main directions can be obtained 0 ，λ 1 And λ 2 Three eigenvalues representing a covariance matrix C, where 0 ≤λ 1 ≤λ 2 Defining a minimum eigenvalue λ 0 The ratio of the total of all characteristic values of the covariance matrix C to the curved surface bending degree eta of the scattered point cloud κ The expression is as follows:
Figure BDA0001886638080000051
wherein, kappa is the degree of curve bending eta calculated κ The number of neighboring points used. Eta κ Quantitatively reflects the bending degree of the curved surface at the point, and when the local point cloud data are on the same plane, eta is κ =0; and when the point cloud is distributed isotropically,
Figure BDA0001886638080000052
and 2, step: concave-convex property for describing fracture surface contour curve based on neighborhood area
As shown in FIG. 2, S r (p) the neighborhood area of a point p on the fracture surface profile curve is expressed, the neighborhood A of the point p is a circular area taking p as the circle center r as the radius and is marked as A r (p) of the formula (I). The integral function f (x) is a linear function, and f (x) =1 when the point x is outside the contour curve and f (x) =0 when the point x is inside the contour curve. Thus, the neighborhood area S of a point p on the fracture surface profile r (p) can be expressed as:
Figure BDA0001886638080000053
S r the geometric meaning of (p) is the circular area A r (p) the area of the outer part of the fracture surface profile, also called the neighborhood area. S r The value of (p) is proportional to the degree of unevenness of the profile curve in the vicinity of the point p and the magnitude of r, and A r (p) S of noise point pairs inside r (p) size has no effect, S is seen r (p) reflects the degree of concavity and convexity of the fracture surface profile curve in the neighborhood of point p. When the point p is a convex vertex point,
Figure BDA0001886638080000054
when point p is a concave vertex, it is true that>
Figure BDA0001886638080000055
When point p is the vertex of a plane, then>
Figure BDA0001886638080000056
And step 3: calculating similarity of fracture surface contour curve based on fuzzy common segment
Due to the complexity of the fracture surface profile curve and the error of discrete sampling, the probability of complete matching of the two profile curves is very small, the similarity of the fracture surface profile curve can be described by adopting a fuzzy commonality segment, and the fuzzy commonality segment refers to searching a section of curve with similar intervals in the two profile curves, on the premise of course that the interval distance cannot be too large. A contour curve E of fracture surface 1i There are m vertices, which can be denoted as
Figure BDA0001886638080000057
The neighborhood area of each vertex is calculated to obtain the characteristic sequence of the vertex as->
Figure BDA0001886638080000058
Another fracture surface contour curve E 2j There are n vertices that can be recorded as->
Figure BDA0001886638080000059
Get special through the same principleSign sequence->
Figure BDA00018866380800000510
Profile curve of fracture surface E 1i The upper vertex->
Figure BDA00018866380800000511
And fracture surface profile curve E 2j The upper vertex->
Figure BDA00018866380800000512
The similar distance of (d) may be expressed as:
Figure BDA0001886638080000061
finding a sequence of features
Figure BDA0001886638080000062
And a sequence of features
Figure BDA0001886638080000063
The fuzzy commonality fragment of (a) can be recursively calculated according to the following formula:
Figure BDA0001886638080000064
wherein H [ i][j]And defining a fuzzy coefficient delta as the maximum separation distance allowed by subscripts i and j, namely the number of times of different characteristic value situations allowed to occur between the two characteristic sequences, for the lengths of fuzzy common segments of the characteristic sequence X and the characteristic sequence Y, wherein the matching precision of the two characteristic sequences can be controlled by the fuzzy coefficient delta. Defining a fracture surface contour curve E 1i And fracture surface profile curve E 2j The similarity of (A) is as follows:
Figure BDA0001886638080000065
calculating a profile piecewise curve E 1i And contour piecewise curve E 2j Because a fragment may have a plurality of fracture surfaces, the algorithm calculates the similarity between any two fracture surfaces of a pair of fragments, and selects the fracture surface with the highest similarity for the next alignment and splicing.
And 4, step 4: alignment splicing of three-dimensional fragments based on iteration nearest point algorithm
Given two sets of points to be registered
Figure BDA0001886638080000066
And &>
Figure BDA0001886638080000067
T M And T N The number of points of the point sets M and N are respectively expressed, and if three-dimensional rigid body transformation is satisfied between the points, the distance between the points can be described as follows:
Figure BDA0001886638080000068
wherein R is a rotation matrix and t is a translation matrix. In each iteration process, the iterative closest point algorithm establishes the correlation between points closest to M in N by searching for the points closest to M, so as to realize rigid body transformation. The basic steps of the iteration are as follows:
(1) From the known rigid body transformation R of step k-1 k-1 And t k-1 First, the point set M is subjected to R k-1 m i +t k-1 Transforming and then re-establishing a correlation r between the two sets of points k (i) The mathematical description is:
Figure BDA0001886638080000069
wherein i =1,2, …, T M 。
(2) And calculating rigid body transformation of the point sets M and N, wherein the mathematical description is as follows:
Figure BDA0001886638080000071
(3) And (3) repeating the step (1) and the step (2) until an iteration termination condition is reached.
And updating the fracture surface of the spliced three-dimensional fragment, and then re-matching the updated fracture surface with the fracture surface of the next three-dimensional fragment until the splicing process of the three-dimensional fragment is completed, thereby finally obtaining the three-dimensional recovery model.

Claims (2)

1. The reconstruction restoration method of the three-dimensional fragments based on the maximum similarity matching is characterized in that a data processing object of the reconstruction restoration method is point cloud data of the three-dimensional fragments acquired by a three-dimensional laser scanner, and the method comprises the following steps:
step 1: based on the point cloud and the neighborhood structure curved surface, calculating the bending degree of the curved surface so as to extract a contour curve of the three-dimensional fragment fracture surface;
step 2: calculating the neighborhood area on the fracture surface contour curve, and describing the concave-convex property of the fracture surface contour curve based on the neighborhood area;
and 3, step 3: searching fuzzy common segments of the fracture surface contour curve, and calculating the similarity of the fracture surface contour curve;
and 4, step 4: performing alignment splicing on the three-dimensional fragments by adopting an iterative closest point algorithm;
in the step 3, fuzzy common segments of the fracture surface contour curve are searched, and the similarity of the fracture surface contour curve is calculated by the following method:
due to the complexity of the fracture surface contour curve and the error of discrete sampling, the probability that the two contour curves are completely matched is very low, the similarity of the fracture surface contour curve is described by adopting a fuzzy common segment, the fuzzy common segment refers to a segment of curve with similar intervals in the two contour curves, and the premise is that the interval distance cannot be too large; a contour curve E of fracture surface 1i There are m vertices, denoted
Figure FDA0003913215890000011
Calculating the neighborhood area of each vertex to obtainCharacterized in that it has a characteristic sequence of->
Figure FDA0003913215890000012
Another fracture surface contour curve E 2j Total n vertices, denoted as
Figure FDA0003913215890000013
The characteristic sequence is obtained by the same way>
Figure FDA0003913215890000014
Profile curve of fracture surface E 1i The upper vertex->
Figure FDA0003913215890000015
And fracture surface profile curve E 2j The upper vertex->
Figure FDA0003913215890000016
The similar distances of (d) are expressed as:
Figure FDA0003913215890000017
finding a sequence of features
Figure FDA0003913215890000018
And a sequence of features
Figure FDA0003913215890000019
Length of fuzzy common fragment of (1) H [ i ]][j]Defining a fuzzy coefficient delta as the maximum interval distance allowed by subscripts i and j, namely the number of times of different characteristic value conditions allowed to appear between the two characteristic sequences, and controlling the matching precision of the two characteristic sequences through the fuzzy coefficient delta; defining a fracture surface contour curve E 1i And fracture surface profile curve E 2j The similarity of (A) is as follows:
Figure FDA00039132158900000110
calculating a profile piecewise curve E 1i And a contour piecewise curve E 2j Because one fragment may have a plurality of fracture surfaces, the algorithm calculates the similarity between any two fracture surfaces of a pair of fragments, and selects the fracture surface with the highest similarity for the next alignment and splicing.
2. The method for regrouping and restoring three-dimensional fragments based on maximum similarity matching as claimed in claim 1, wherein the neighborhood area on the fracture surface contour curve is calculated in the step 2, and the concave-convex property of the fracture surface contour curve is described based on the neighborhood area by adopting the following method S r (p) the neighborhood area of a point p on the fracture surface profile curve is expressed, the neighborhood A of the point p is a circular area taking p as the circle center r as the radius and is marked as A r (p); the integral function f (x) is an exemplary function, and f (x) =1 when the point x is outside the contour curve, and f (x) =0 when the point x is inside the contour curve; neighborhood area S of a point p on the fracture surface profile r (p) is represented by:
Figure FDA0003913215890000021
S r the geometric meaning of (p) is the circular area A r (p) the area of the outer part of the fracture surface profile curve, also called the neighborhood area; s r The value of (p) is proportional to the degree of irregularity of the profile curve in the vicinity of the point p and the magnitude of r, and A r (p) S of noise point pairs inside r (p) size has no effect, S is seen r (p) the concave-convex degree of the fracture surface profile curve in the neighborhood of the point p is reflected; when the point p is a convex vertex point,
Figure FDA0003913215890000022
when point p is a concave vertex, it is true that>
Figure FDA0003913215890000023
When point p is the vertex of a plane, then>
Figure FDA0003913215890000024
/>
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